Exams › JEE Advanced › Physics

A uniform disc is hinged at its centre and connected to a spring (spring constant K = 900 N/m) at a point on its rim that is a distance d = 2 m below the axle. The system is in equilibrium. If the disc is rotated through a small angle theta0 = 3 degrees from equilibrium, find the maximum kinetic energy (in joules) of the disc. (Given: disc radius R = 3 m, pi² = 10)

1. 0.5
2. 1.0
3. 1.5
4. 2.0

Correct answer: 1.0

Solution

When the disc rotates by small angle theta, the spring (attached at distance d below centre) stretches by x = d*theta. Spring PE = (1/2)*K*(d*theta)². Maximum KE = maximum PE (energy conservation in SHM, starting from rest at theta0). Note: the disc radius R and pi² = 10 are given; R may be needed if the spring is attached at rim (d = R would give d = 3m, but d = 2m is given separately). Since the problem specifies d = 2m explicitly, use d = 2m.

Related JEE Advanced Physics questions

• A particle constrained to move along the x-axis has a potential energy described by U(x) = k[1 - exp(-x²)], where k is a positive constant and -∞ ≤ x ≤ +∞. Which of the following statements is true?
• What is the increase in potential energy of a spring when it is stretched or compressed by a distance x from its equilibrium position?
• A particle executes SHM of amplitude A and angular frequency omega along a straight line. When it is at a distance (sqrt(3)/2)A from the mean position, an impulsive force instantaneously increases its kinetic energy by (1/2)m*omega²*A². What is the new amplitude of oscillation?
• Two particles P and Q each perform SHM along the same straight line. Their displacements are given by y_P = A sin(omega*t + phi₁) and y_Q = A cos(omega*t + phi₂). At t = 0, particle P is at displacement A/sqrt(2) from mean position and moving toward positive displacement (rightward), while particle Q is at displacement (sqrt(3)/2)*A and moving toward negative displacement (leftward). What is the value of (phi₂ - phi₁)?
• A disc performs angular (torsional) oscillations using a wire with torsional constant k. Its initial angular amplitude is theta0. At the instant when the disc passes through angular displacement theta0/2 (half the amplitude), an impulsive torque is applied that instantaneously increases its angular velocity to 1.5 times its value at that position. Find the new angular amplitude of oscillation after the impulse.
• A particle undergoes simple harmonic motion with time period T. At a certain instant its speed is 60% of its maximum speed and is increasing. A time interval deltaₜ later, its speed becomes 80% of its maximum speed and is now decreasing. What is the smallest possible value of deltaₜ?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →